Non-Intrusive Underwater Measurement of Local Scour Around a Bridge Pier

: A non-intrusive low-cost technique for monitoring the temporal and spatial evolution of the scour hole around bridge piers is presented. The setup for the application of the technique is simple, low-cost and non-intrusive. It couples a line laser source and commercial camera to get a fast and accurate measurement of the whole scour hole in the front and behind the bridge pier. A short campaign of measurements of the scour hole around a bridge pier in clear-water conditions is presented to provide a control test and to show how to apply the new method. Finally, the results are compared with two of the most used equations, for the time evolution of the maximum scour depth in clear-water conditions, to show the e ﬀ ectiveness of the proposed technique.


Introduction
Scouring at bridge piers and river abutments is one of the main causes of bridge failures, causing major losses to the road networks and rail infrastructures [1][2][3][4][5][6]. Local scour, which is the purpose of this work, is due to vortices forming at the base of pier impacted by the water current. This process is time-dependent and, despite the research efforts during the last five decades, the time evolution of scour depth remains a subject of concern for hydraulic engineers and researchers. The main problem from the experimental point of view is that this phenomenon requires thorough spatial investigation and continuous monitoring of the morphological characteristics of the riverbed.
In general, the equilibrium between flow erosion capability and the resistance to motion of the bed is gradually reached through the adjustment of the bottom boundary which imposes the depth of scour hole and its three-dimensional shape around the piers [7][8][9]. While in live-bed conditions this equilibrium is very rapidly achieved and oscillates due to the passage of bed-forms in clear-water conditions the process is rather slow or never reached [10][11][12][13]. According to a large number of experimental studies, the equilibrium is reached in finite time [2,14]. However, few authors argue that equilibrium can be reached only asymptotically [15]. Research on local scouring has been made mostly through laboratory experimentation and, in the last decades, a large number of runs have been carried out for evaluating bridge vulnerability to scour under several experimental conditions (pier diameter, water velocity and depth, grain diameter, etc.) [2,9,[13][14][15][16][17][18][19][20][21].
From an engineering point of view, once the design of the pier is done (shape of the pier and its orientation with respect to the flow), and the extreme flow conditions are chosen, the relevant questions are those connected not only with the maximum depth of the scour but also with the shape and dimension of the whole scour hole. Scour and deposition are both central in bridge design. While, as stated above, local scour mechanism is often responsible for bridge failure, the dunes, that grow in the wake of the bridge piers and fed by scoured bed material, are relevant in river control engineering as they can become significant obstacles for the flow downstream of bridges [22]. Very few systematic analysis. According to the authors the method, that can operate only on small areas, has some limitations due to the roughness of the water surface, high turbidity, illuminance and specular reflection from the target surface.
The objective of this study is to present a new method, easy to use, inexpensive and non-intrusive, for continuous acquisition of the 2-D temporal variation of the scour hole shape around a cylindrical bridge pier for uniform sediment and steady clear-water flow. The technique is based on the use of a continuous-wave laser source and a camera. In particular, the green beam emitted by the laser source is refracted by a cylindrical lens to create a vertical laser sheet, parallel to the channel walls, and crossing radially the Plexiglas pier. The camera is placed laterally to the flume and, thanks to a simple calibration methodology, acquires the evolution of the scour hole. The design idea is not completely original but is similar to that used for very expensive systems such as the PIV [46]. The differences are to be found in the large area swept by the acquisition system and in the very low cost of the instrumentation, which can cost a few hundred euros. Although in the present work the method is applied to a 2-D case, it can be easily, through the use of more laser sheets, extended to three-dimensional measurements. To show the potential of the method, four experimental tests were carried out varying only the water velocity (U) and maintaining constant the water depth (h 0 ), the type of sand and the diameter of the bridge pier (D). Finally, two of the most used equations for the evolution of the maximum scour depth in clear-water conditions [2,16] are compared using the data obtained in the four runs using the new technique.

Experimental Design and Flume
The experiments were conducted in a flume, 0.50 m wide, 0.60 m deep and 12 m long glass-sided rectangular channel with 0.5% sloping, of the Hydraulic Laboratory at the Politecnico di Torino (IT). The water is recirculated in the flume using a low and constant head reservoir, and the flow is regulated by a high precision hydraulic gate placed between the reservoir and the flume. The flow rate is measured using an electromagnetic flow gauge (PROMAG W, Endress-Hauser, Reinach, Switzerland) placed on the recirculating pipe downstream the hydraulic gate.
The water, after passing through the flume, falls into the main recirculation channel of the laboratory and is sent back to the low head tank. This recirculation system, shown in Figure 1, guarantees a constant flow rate throughout the experiment. To guarantee the water level, a sluicegate is placed at the end of the flume. The erodible bed has been obtained in the central part of channel where a 3 m long test section is built placing a 0.27 m thick layer of uniform quartz sand (ρ s = 2650 kg/m 3 ; d 50 = 1.25 mm).
Water 2019, 11, x FOR PEER REVIEW  3 of 11 areas, has some limitations due to the roughness of the water surface, high turbidity, illuminance and specular reflection from the target surface. The objective of this study is to present a new method, easy to use, inexpensive and nonintrusive, for continuous acquisition of the 2-D temporal variation of the scour hole shape around a cylindrical bridge pier for uniform sediment and steady clear-water flow. The technique is based on the use of a continuous-wave laser source and a camera. In particular, the green beam emitted by the laser source is refracted by a cylindrical lens to create a vertical laser sheet, parallel to the channel walls, and crossing radially the Plexiglas pier. The camera is placed laterally to the flume and, thanks to a simple calibration methodology, acquires the evolution of the scour hole. The design idea is not completely original but is similar to that used for very expensive systems such as the PIV [46]. The differences are to be found in the large area swept by the acquisition system and in the very low cost of the instrumentation, which can cost a few hundred euros. Although in the present work the method is applied to a 2-D case, it can be easily, through the use of more laser sheets, extended to three-dimensional measurements. To show the potential of the method, four experimental tests were carried out varying only the water velocity ( ) and maintaining constant the water depth (ℎ 0 ), the type of sand and the diameter of the bridge pier ( ). Finally, two of the most used equations for the evolution of the maximum scour depth in clear-water conditions [2,16] are compared using the data obtained in the four runs using the new technique.

Experimental Design and Flume
The experiments were conducted in a flume, 0.50 m wide, 0.60 m deep and 12 m long glass-sided rectangular channel with 0.5% sloping, of the Hydraulic Laboratory at the Politecnico di Torino (IT). The water is recirculated in the flume using a low and constant head reservoir, and the flow is regulated by a high precision hydraulic gate placed between the reservoir and the flume. The flow rate is measured using an electromagnetic flow gauge (PROMAG W, Endress-Hauser, Reinach, Switzerland) placed on the recirculating pipe downstream the hydraulic gate.
The water, after passing through the flume, falls into the main recirculation channel of the laboratory and is sent back to the low head tank. This recirculation system, shown in Figure 1, guarantees a constant flow rate throughout the experiment. To guarantee the water level, a sluicegate is placed at the end of the flume. The erodible bed has been obtained in the central part of channel where a 3 m long test section is built placing a 0.27 m thick layer of uniform quartz sand ( = 2650 kg m 3 ⁄ ; 50 = 1.25 mm).  A Plexiglas transparent cylinder, having a diameter D = 32 mm, is used as a pier and placed in the middle of the test section ( Figure 2). Prior to each experiment, the sand bed on the test section was perfectly leveled. During the experiments, the water depth is kept to h 0 = 215 mm fixing the opening of the sluicegate. In order to avoid undesirable scouring during the unsteady state of the experiment, the flume is filled gradually and water is slowly pumped in the flume through secondary water circuits both upstream and downward of the test section. When the water level reached 215 mm the secondary pumps are stopped and the main pump is switched on.
Water 2019, 11, x FOR PEER REVIEW 4 of 11 A Plexiglas transparent cylinder, having a diameter = 32 mm, is used as a pier and placed in the middle of the test section ( Figure 2). Prior to each experiment, the sand bed on the test section was perfectly leveled. During the experiments, the water depth is kept to ℎ 0 = 215 mm fixing the opening of the sluicegate. In order to avoid undesirable scouring during the unsteady state of the experiment, the flume is filled gradually and water is slowly pumped in the flume through secondary water circuits both upstream and downward of the test section. When the water level reached 215 mm the secondary pumps are stopped and the main pump is switched on. Furthermore, to avoid exceeding, during the initial ramp in the flow rate, the critical velocity on the test section the tailgates remained initially closed, imposing a high water depth and low flow velocity. Only when the flow reached the wished value the tailgates is opened until the final height. This initial transient lasted only a few minutes and it didn't influence the erosive action which was generated around the pier.

Measuring System
In Figures 1 and 2 is also shown the laser sheet that is the main novelty of this work. In particular, above the flume, a continuous wave cyan line laser source (488 nm, 200 mW, Changchun New Industries Optoelectronics Tech. Co., Ltd., Changchun, Jilin, China) is installed. This type of laser is widely used in fluorescence microscopy since its wavelength activates a large number of different dyes, such as Alexa 488, eGFP, SYTO-13 DNA, Chromeo, just to name a few. In our technique, the laser source does not need to have high performance in terms of stability, coherence or beam size. A laser source of a few hundreds of mW (300-400 euros) is more than enough. The green beam emitted by the laser source is refracted by a cylindrical lens to expand the laser light along the longitudinal axis only. The result is a vertical laser sheet, parallel to the channel walls, and positioned, using a high precision carriage plate, in the middle of the channel. Furthermore, the laser sheet crossed radially the transparent Plexiglas pier and intercepts the surface of the moveable test section highlighting its geometry ( Figure 3). Thanks to the fact that the laser sheet crosses the cylinder radially, its optical path is not impacted by refraction, then the laser sheet, upstream and downstream of the cylinder, is everywhere coplanar. To prevent the ripples of the water surface, created by the pile and large-scale turbulence, from altering the verticality of the laser sheet, a transparent Plexiglas slab, 1 cm wide and 60 cm long) is positioned horizontally at the level of the water surface. At the side of the flume, it is placed a digital camera "Canon EOS 400D" remote-controlled by PC set to capture an image at a set time interval. The camera is positioned so that it can frame both the upstream and downstream scour bed. Furthermore, to avoid exceeding, during the initial ramp in the flow rate, the critical velocity on the test section the tailgates remained initially closed, imposing a high water depth and low flow velocity. Only when the flow reached the wished value the tailgates is opened until the final height. This initial transient lasted only a few minutes and it didn't influence the erosive action which was generated around the pier.

Measuring System
In Figures 1 and 2 is also shown the laser sheet that is the main novelty of this work. In particular, above the flume, a continuous wave cyan line laser source (488 nm, 200 mW, Changchun New Industries Optoelectronics Tech. Co., Ltd., Changchun, Jilin, China) is installed. This type of laser is widely used in fluorescence microscopy since its wavelength activates a large number of different dyes, such as Alexa 488, eGFP, SYTO-13 DNA, Chromeo, just to name a few. In our technique, the laser source does not need to have high performance in terms of stability, coherence or beam size. A laser source of a few hundreds of mW (300-400 euros) is more than enough. The green beam emitted by the laser source is refracted by a cylindrical lens to expand the laser light along the longitudinal axis only. The result is a vertical laser sheet, parallel to the channel walls, and positioned, using a high precision carriage plate, in the middle of the channel. Furthermore, the laser sheet crossed radially the transparent Plexiglas pier and intercepts the surface of the moveable test section highlighting its geometry (Figure 3). Thanks to the fact that the laser sheet crosses the cylinder radially, its optical path is not impacted by refraction, then the laser sheet, upstream and downstream of the cylinder, is everywhere coplanar. To prevent the ripples of the water surface, created by the pile and large-scale turbulence, from altering the verticality of the laser sheet, a transparent Plexiglas slab, 1 cm wide and 60 cm long) is positioned horizontally at the level of the water surface. At the side of the flume, it is placed a digital camera "Canon EOS 400D" remote-controlled by PC set to capture an image at a set time interval. The camera is positioned so that it can frame both the upstream and downstream scour bed. Processing this sequence of images, it is possible to obtain the scour hole evolution during the experiment. For this purpose there are three critical issues to face: (1) Identify, in each image, the footprint of the laser sheet on the sand bottom, (2) converting pixels into distances, and (3) adjusting the image distortions due to the camera lens and to the optical path of the light refracted when double-crossing two different mediums (water-glass and glass-air). The identification of the laser footprint on the bottom is a rather simple and straight forward task when the laser intensity has been correctly set and the dark conditions imposed on the channel. In particular, the laser power must not be too low, or the footprint would be unidentifiable, neither too high since it would make the track too thick and the bottom not uniquely identifiable.
Moreover, to avoid disturbances due to the color of the sand, dark conditions are met inside the channel to allow better identification of the laser footprint on the test section. In Figure 4, four photos taken during one of the tests are shown as an example. A code in MATLAB (2019a), based on the intensity of the green light (in the RGB matrix) has been appositely developed and calibrated to identify the footprint, in pixel, on every single photo. Processing this sequence of images, it is possible to obtain the scour hole evolution during the experiment. For this purpose there are three critical issues to face: (1) Identify, in each image, the footprint of the laser sheet on the sand bottom, (2) converting pixels into distances, and (3) adjusting the image distortions due to the camera lens and to the optical path of the light refracted when double-crossing two different mediums (water-glass and glass-air). The identification of the laser footprint on the bottom is a rather simple and straight forward task when the laser intensity has been correctly set and the dark conditions imposed on the channel. In particular, the laser power must not be too low, or the footprint would be unidentifiable, neither too high since it would make the track too thick and the bottom not uniquely identifiable.
Moreover, to avoid disturbances due to the color of the sand, dark conditions are met inside the channel to allow better identification of the laser footprint on the test section. In Figure 4, four photos taken during one of the tests are shown as an example. A code in MATLAB (2019a), based on the intensity of the green light (in the RGB matrix) has been appositely developed and calibrated to identify the footprint, in pixel, on every single photo.  Processing this sequence of images, it is possible to obtain the scour hole evolution during the experiment. For this purpose there are three critical issues to face: (1) Identify, in each image, the footprint of the laser sheet on the sand bottom, (2) converting pixels into distances, and (3) adjusting the image distortions due to the camera lens and to the optical path of the light refracted when double-crossing two different mediums (water-glass and glass-air). The identification of the laser footprint on the bottom is a rather simple and straight forward task when the laser intensity has been correctly set and the dark conditions imposed on the channel. In particular, the laser power must not be too low, or the footprint would be unidentifiable, neither too high since it would make the track too thick and the bottom not uniquely identifiable.
Moreover, to avoid disturbances due to the color of the sand, dark conditions are met inside the channel to allow better identification of the laser footprint on the test section. In Figure 4, four photos taken during one of the tests are shown as an example. A code in MATLAB (2019a), based on the intensity of the green light (in the RGB matrix) has been appositely developed and calibrated to identify the footprint, in pixel, on every single photo.

Calibration and Image Processing
Distortion is inherent in all images taken through lens systems. The classical Brown lens distortion model is used to determine where any point in the distorted image would appear in the image plane if there were no lens distortion [47]. A three-millimeter sandwich panel with a core in aluminium honeycomb bonded to two skins of the aluminium panel is used as a calibration plate. This material was chosen for its lightness and rigidity. Furthermore, being entirely in aluminium, it can be used in complete immersion conditions. A checkerboard pattern (5 mm by 5 mm) was drawn on one surface of the plate using laser engraving. The calibration plate is used both for the image calibration and, at the beginning of each experimental test, as an absolute reference system in the vertical section of the laser sheet. Once the calibration plate is placed, in still water, few photos are taken without the pier. Finally, the calibration plate is removed from the flume, the pier is installed into the sad bed, and the experiment is started.
In Figure 5 the profiles of the bottom, acquired at several time instants from 0 to 24 h, are shown. As expected, the extension of the scour and its maximum depth increase as the flow rate increases. To quantitatively verify the results obtained with this new experimental technique, in the next paragraph, the comparisons between the maximum scour depth measured and that predicted by some of the most used equations are shown.

Calibration and Image Processing
Distortion is inherent in all images taken through lens systems. The classical Brown lens distortion model is used to determine where any point in the distorted image would appear in the image plane if there were no lens distortion [47]. A three-millimeter sandwich panel with a core in aluminium honeycomb bonded to two skins of the aluminium panel is used as a calibration plate. This material was chosen for its lightness and rigidity. Furthermore, being entirely in aluminium, it can be used in complete immersion conditions. A checkerboard pattern (5 mm by 5 mm) was drawn on one surface of the plate using laser engraving. The calibration plate is used both for the image calibration and, at the beginning of each experimental test, as an absolute reference system in the vertical section of the laser sheet. Once the calibration plate is placed, in still water, few photos are taken without the pier. Finally, the calibration plate is removed from the flume, the pier is installed into the sad bed, and the experiment is started.
In Figure 5 the profiles of the bottom, acquired at several time instants from 0 to 24 h, are shown. As expected, the extension of the scour and its maximum depth increase as the flow rate increases. To quantitatively verify the results obtained with this new experimental technique, in the next paragraph, the comparisons between the maximum scour depth measured and that predicted by some of the most used equations are shown.

Existing Equations for Temporal Scour Depth
Several formulae and mathematical models developed for the estimation of the scour depth are still primarily based on theoretical approaches and laboratory tests [2,10,14,16,18,20,48]. This justifies the fact that, in the last decades, a plethora of numerical and laboratory investigations have been conducted to quantify the maximum scour depth at bridge piers. From this large amount of data,

Existing Equations for Temporal Scour Depth
Several formulae and mathematical models developed for the estimation of the scour depth are still primarily based on theoretical approaches and laboratory tests [2,10,14,16,18,20,48]. This justifies the fact that, in the last decades, a plethora of numerical and laboratory investigations have been conducted to quantify the maximum scour depth at bridge piers. From this large amount of data, several equations are available for estimating temporal and equilibrium scour depth. Most of these investigations have been focused on equilibrium scour depth and very fewer formulae are available for estimating the temporal evolution of the scour depth [2,15,16,18,49,50]. It is not our intention to remember, in this work, all the formulations or to decide which is the best. The equations are used here to verify if the results obtained by the proposed technique align with the most reliable equations used in the past. In the present study, the temporal scour depth equations proposed by Oliveto and Hager [16] and Melville and Chiew [2] are chosen for evaluating the accuracy of our data.
Oliveto and Hager [17] proposed a scour equation that involves the scour depth z as a function of time t. They observed that the densimetric particle Froude number (F d ) is the dominant parameter controlling the scour process and can be made explicit through the following scaling relationship.
where U is the bulk approach velocity, ρ s and ρ are the sediment and fluid densities, g is the gravitational acceleration, and d 50 is the median grain size. Note that F d can also be expressed as the ratio of U and a reference velocity U R = [g(ρ s /ρ − 1)d 50 ] 1/2 . Similarly, Oliveto and Hager [17] proposed a reference length for piers L R = D α h 0 β , with α + β = 1, and, consequently, a reference time T R = L R /U R . The dimensionless depth and time of scour can be written as: As well, With, as suggested by the authors, α = 2/3 and β =1/3. Finally, based on a detailed data analysis conducted by Oliveto and Hager [17], and subsequently verified using more data by Pandey et al. [19], the dimensionless scour depth variation Z can be parameterized as With σ = (d 84 /d 16 ) 1/2 as the sediment uniformity parameter. Melville and Chiew [2] proposed a time-dependent scour depth equation built around a large dataset of experimental laboratory data and reads as follows: where and Z e and T e are respectively the equilibrium scour depth and time (in days), and U c denote the critical velocity at the threshold condition for sediment movement defined by Lauchlan and Melville [48]. Unlike what was assumed by Oliveto and Hager [17], the expression by Melville and Chiew [2] assumes that the scouring will reach an equilibrium condition. The general expression for these two equilibrium parameters can be found in [2], in our case study the are As well, Note that, this expression for T e is valid for a flow shallowness h 0 /D > 6. In our case, the flow shallowness is 6.7, then the maximum scour depth, according to Melville and Chiew [2], should not depend on the water depth but, unlike the formula by Oliveto and Hager [17], only on the pier diameter, incoming velocity and sand median size.

Comparison with Existing Equations
The two equations are compared in this study with clear-water temporal scour obtained in the four runs described above. The accuracy of these equations are here checked graphically in Figure 6 where the time records of the scour depths are plotted along with the estimations from Oliveto and Hager [16], as a solid line, and Melville and Chiew [2], as dash-dot line. The inspection of this figure reveals that the equation proposed by Oliveto and Hager [16] describes the data very well when the excavation is fully developed (t > 10 h). Although the temporal duration of the experiments does not allow a clear picture, the scour depth, as predicted by Oliveto and Hager [16], does not seem to reach a state of equilibrium. In particular, the temporal growth of scour depth seems to be of a logarithmic type as previously predicted [16,51,52]. On the contrary, the equation by Melville and Chiew [2] best describes the data in the first part of the temporal development of the scouring process.
Water 2019, 11, x FOR PEER REVIEW 8 of 11

Comparison with Existing Equations
The two equations are compared in this study with clear-water temporal scour obtained in the four runs described above. The accuracy of these equations are here checked graphically in Figure 6 where the time records of the scour depths are plotted along with the estimations from Oliveto and Hager [16], as a solid line, and Melville and Chiew [2], as dash-dot line. The inspection of this figure reveals that the equation proposed by Oliveto and Hager [16] describes the data very well when the excavation is fully developed (t > 10 h). Although the temporal duration of the experiments does not allow a clear picture, the scour depth, as predicted by Oliveto and Hager [16], does not seem to reach a state of equilibrium. In particular, the temporal growth of scour depth seems to be of a logarithmic type as previously predicted [16,51,52]. On the contrary, the equation by Melville and Chiew [2] best describes the data in the first part of the temporal development of the scouring process. The time evolution of the maximum scour depth measured in the four runs are shown, in the coordinates suggested by Oliveto and Hager [16], in Figure 7. As expected by the previous considerations, the inspection of Figure 7 reveals that the suggested predictor describes the scour depth time evolution quite well for > 4 · 10 3 . The time evolution of the maximum scour depth measured in the four runs are shown, in the coordinates suggested by Oliveto and Hager [16], in Figure 7. As expected by the previous considerations, the inspection of Figure 7 reveals that the suggested predictor describes the scour depth time evolution quite well for T > 4·10 3 .

Conclusions
A new technique for measuring the 2-D shape of an evolving scour hole has been presented. The technique is based on the use of line laser source and a commercial camera that acquires the bed evolution during the experiment. The method is described in each step, and an extended guideline for the use of the technique is provided in the paper, both in terms of experimental design and data post-processing. The intuitive methodology and the very low-cost setup make this experimental method applicable not only to scouring but also to an extensive variety of experiments where the bed is evolving in time and space. To provide a better understanding of the method and a preliminary proof of its capabilities, it has been used to carry out a short experimental measurement campaign about the time evolution of a sour hole around a bridge pier. The results have been compared with two of the most used equations for the evolution of the maximum scour depth in clear-water conditions.

Conclusions
A new technique for measuring the 2-D shape of an evolving scour hole has been presented. The technique is based on the use of line laser source and a commercial camera that acquires the bed evolution during the experiment. The method is described in each step, and an extended guideline for the use of the technique is provided in the paper, both in terms of experimental design and data post-processing. The intuitive methodology and the very low-cost setup make this experimental method applicable not only to scouring but also to an extensive variety of experiments where the bed is evolving in time and space. To provide a better understanding of the method and a preliminary proof of its capabilities, it has been used to carry out a short experimental measurement campaign about the time evolution of a sour hole around a bridge pier. The results have been compared with two of the most used equations for the evolution of the maximum scour depth in clear-water conditions.